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Designation: D 2244 – 05



Standard Practice for



Calculation of Color Tolerances and Color Differences from Instrumentally Measured Color Coordinates1 This standard is issued under the fixed designation D 2244; the number immediately following the designation indicates the year of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscript epsilon (e) indicates an editorial change since the last revision or reapproval. This standard has been approved for use by agencies of the Department of Defense.



INTRODUCTION



This practice originally resulted from the consolidation of a number of separately published methods for the instrumental evaluation of color differences. As revised in 1979, it included four color spaces in which color-scale values could be measured by instruments, many of which were obsolete, and the color differences calculated by ten equations for different color scales. The sections on apparatus, calibration standards and methods, and measurement procedures served little purpose in the light of modern color-measurement technology. The revision published in 1993 omitted these sections, and limited the color spaces and color-difference equations considered, to the three most widely used in the paint and related coatings industry. A previous revision added two new color tolerance equations and put two of the color difference equations from the 1993 version in an informative appendix for historical purposes. the correlation between the magnitude of a measured color difference and its commercial acceptability. 1.3 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory requirements prior to use.



1. Scope* 1.1 This practice covers the calculation, from instrumentally measured color coordinates based on daylight illumination, of color tolerances and small color differences between opaque specimens such as painted panels, plastic plaques, or textile swatches. Where it is suspected that the specimens may be metameric, that is, possess different spectral curves though visually alike in color, Practice D 4086 should be used to verify instrumental results. The tolerances and differences determined by these procedures are expressed in terms of approximately uniform visual color perception in CIE 1976 CIELAB opponent-color space (1)2, CMC tolerance units (2), CIE94 tolerance units (3), the DIN99 color difference formula given in DIN 6176 (4), or the new CIEDE2000 color difference units (5). 1.2 For product specification, the purchaser and the seller shall agree upon the permissible color tolerance between test specimen and reference and the procedure for calculating the color tolerance. Each material and condition of use may require specific color tolerances because other appearance factors, (for example, specimen proximity, gloss, and texture), may affect



2. Referenced Documents 2.1 ASTM Standards: 3 D 1729 Practice for Visual Appraisal of Colors and Color Differences of Diffusely-Illuminated Opaque Materials D 4086 Practice for Visual Evaluation of Metamerism E 284 Terminology of Appearance E 308 Practice for Computing the Colors of Objects by Using the CIE System E 805 Practice for Identification of Instrumental Methods of Color or Color-Difference Measurement of Materials E 1164 Practice for Obtaining Spectrometric Data for Object-Color Evaluation 2.2 Other Standards: DIN 6176 Farbmetrische, Bestimmung von Farbabständen bei Körperfarben nach der DIN99-Formel4



1 This practice is under the jurisdiction of ASTM Committee E12 on Color and Appearance and is the direct responsibility of Subcommittee E12.04 on Color and Appearance Analysis. Current edition approved Oct. 1, 2005. Published November 2005. Originally approved in 1964. Last previous edition approved in 2002 as D 2244 – 02e1. 2 The boldface numbers in parentheses refer to the list of references at the end of this standard.



3 For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [email protected]. For Annual Book of ASTM Standards volume information, refer to the standard’s Document Summary page on the ASTM website. 4 Available from Beuth Verlag GmbH, 10772 Berlin, Germany.



*A Summary of Changes section appears at the end of this standard. Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.



1



D 2244 – 05 had weighting factors applied to provide some degree of uniformity so that color differences in various regions of color space will be more nearly comparable. On the other hand, color differences obtained for the same specimens evaluated in different color-scale systems are not likely to be identical. To avoid confusion, color differences among specimens or the associated tolerances should be compared only when they are obtained for the same color-scale system. There is no simple factor that can be used to convert accurately color differences or color tolerances in one system to difference or tolerance units in another system for all colors of specimens. 5.2 For uniformity of practice, the CIE recommended in 1976 the use of two color metrics. The CIELAB metric, with its associated color-difference equation, has found wide acceptance in the coatings, plastics, textiles and related industries. While the CIELAB equation has not completely replaced the use of Hunter LH, aH, bH, this older scale is no longer recommended for other than legacy users, and is therefore included in an Appendix for historical purposes. The CIELAB color-difference equation is also not recommended in this practice for use in describing small and moderate color differences (differences with magnitude less than 5.0 D E*ab units). The four more recently defined equations, documented here, are highly recommended for use with color-differences in the range of 0.0 to 5.0 DE*ab units. 5.3 Users of color tolerance equations have found that, in each system, summation of three, vector color-difference components into a single scalar value is very useful for determining whether a specimen color is within a specified tolerance from a standard. However, for control of color in production, it may be necessary to know not only the magnitude of the departure from standard but also the direction of this departure. It is possible to include information on the direction of a small color difference by listing the three instrumentally determined components of the color difference. 5.4 Selection of color tolerances based on instrumental values should be carefully correlated with a visual appraisal of the acceptability of differences in hue, lightness, and saturation obtained by using Practice D 1729. The three tolerance equations given here have been tested extensively against such data for textiles and plastics and have been shown to agree with the visual evaluations to within the experimental uncertainty of the visual judgments. That implies that the equations themselves misclassify a color difference with a frequency no greater than that of the most experienced visual color matcher. 5.5 While color difference equations and color tolerance equations are routinely applied to a wide range of illuminants, they have been derived or optimized, or both, for use under daylight illumination. Good correlation with the visual judgments may not be obtained when the calculations are made with other illuminants. Use of a tolerance equation for other than daylight conditions will require visual confirmation of the level of metamerism in accordance with Practice D 4086.



3. Terminology 3.1 Terms and definitions in Terminology E 284 are applicable to this practice. 3.2 Definitions of Terms Specific to This Standard: 3.2.1 colorimetric spectrometer, n—spectrometer, one component of which is a dispersive element (such as a prism, grating or interference filter or wedge or tunable or discrete series of monochromatic sources), that is normally capable of producing as output colorimetric data (such as tristimulus values and derived color coordinates or indices of appearance attributes). Additionally, the colorimetric spectrometer may also be able to report the underlying spectral data from which the colorimetric data were derived. 3.2.1.1 Discussion—At one time, UV-VIS analytical spectrophotometers were used for colorimetric measurements. Today, while instruments intended for use in color measurements share many common components, UV-VIS analytical spectrophotometers are designed to optimize their use in chemometric quantitative analysis, which requires very precise spectral position and very narrow bandpass and moderate baseline stability. Colorimetric spectrometers are designed to optimize their use as digital simulations of the visual colorimeter or as the source of spectral and colorimetric information for computer-assisted color matching systems. Digital colorimetry allows more tolerance on the spectral scale and spectral bandwidth but demand much more stability in the radiometric scale. 3.2.2 color tolerance equation, n—a mathematical expression, derived from acceptability judgments, which distorts the metric of color space based on the coordinates in that color space, of a reference color, for the purpose of single number shade passing. 3.2.2.1 Discussion—The color tolerance equation computes a pass/fail value based on which of the pair of specimens is assigned the designation “standard.” Thus, inter-changing the reference and test specimens will result in a change in the predicted level of acceptance between the specimens while the perceived difference is unchanged. A color difference equation quantifies distance in a color space using the metric of that space. Inter-changing the reference and test specimens does not change either the perceived or predicted color differences. 4. Summary of Practice 4.1 The differences in color between a reference and a test specimen are determined from measurements made by use of a spectral based or filter based colorimeter. Reflectance readings from spectral instruments are converted by computations to color-scale values in accordance with Practice E 308, or these color-scale values may be read directly from instruments that automatically make the computations. Color-difference units are computed, from these color-scale values, and approximate the perceived color differences between the reference and the test specimen.



6. Description of Color-Difference and Color-Tolerance Equations



5. Significance and Use 5.1 The original CIE color scales based on tristimulus values X, Y, Z and chromaticity coordinates x, y are not uniform visually. Each subsequent color scale based on CIE values has



6.1 CIE 1931 and 1964 Color Spaces—The daylight colors of opaque specimens are represented by points in a space 2



D 2244 – 05 equations are replaced by the following modified equations for calculations of a* and b*:



formed by three rectangular axes representing the lightness scale Y and chromaticity scales x and y, where:



F S D S DG F S D S DG



X x5X1Y1Z



(1)



X Y a* 5 500 · f X 2 f Y n n



(9)



Y y5X1Y1Z



(2)



Y Z b* 5 200 · f Y 2 f Z n n



(10)



where X, Y, and Z are tristimulus values for either the 1931 CIE standard observer (2° observer) or the 1964 CIE standard observer (10° observer) and standard illuminant D65, or other phase of daylight. These scales do not provide a perceptually uniform color space. Consequently, color differences are seldom if ever computed directly from differences in x, y, and Y. 6.2 CIE 1976 L* a* b* Uniform Color Space and ColorDifference Equation (1, 6)—This is an approximately uniform color space based on nonlinear expansion of the tristimulus values and taking differences to produce three opponent axes that approximate the percepts of lightness-darkness, rednessgreenness and yellowness-blueness. It is produced by plotting in rectangular coordinates the quantities L*, a*, b*, calculated as follows:



S D



Y L* 5 116 · Y n a* 5 500 ·



b* 5 200 ·



1 3



2 16



1 3



Y Yn



2



Y Yn



2



Z Zn



1 3



Y Y f Y 5 Y n n



Z Z f Z 5 Z n n



(4)



(5) (6)



Y Y n $ 0.008856



if



if



Y Yn , 0.008856



Z if Z $ 0.008856 n Z Zn , 0.008856



(12)



(13) (14)



(15) (16)



DL* 5 L*B 2 L* S



(17)



Da* 5 a*B 2 a*S



(18)



Db* 5 b*B 2 b*S



(19)



where L*S, a*S, and b*S refer to the reference or standard, and L*B, a*B, and b*B refer to the test specimen or batch. The signs of the components DL*, Da*, and Db* have the following approximate meanings (7):



(7)



1 DL* 5 lighter



(20)



2DL* 5 darker



(21)



1 Da* 5 redder ~less green!



(22)



2Da* 5 greener ~less red!



(23)



1 Db* 5 yellow ~less blue!



(24)



2D b* 5 bluer ~less yellow!



(25)



6.2.6 For judging the direction of the color difference between two colors, it is useful to calculate their CIE 1976 metric hue angles hab and CIE 1976 metric chroma C*ab as follows:



6.2.2 The CIE 1976 (L* a* b*) metric fails to converge to zero appropriately when one or more of the ratios X/Xn, Y/Yn, and Z/Zn is less than 0.008856. In calculating L*, values of Y/Yn less than 0.008856 may still be utilized if the normal formula is used for values of Y/Yn greater than 0.008856, and the following modified formula is used for values of Y/Yn equal to or less than 0.008856.



S D



X Xn , 0.008856



(11)



6.2.4 The magnitude, DE*ab, gives no indication of the character of the difference since it does not indicate the relative quantity and direction of hue, chroma, and lightness differences. 6.2.5 The direction of the color difference is described by the magnitude and algebraic signs of the components DL*, Da*, and Db*:



NOTE 1—The color space defined above is called the CIE 1976 L* a * b* space and the color-difference equation the CIE 1976 L* a* b* color-difference formula. The abbreviation CIELAB (with all letters capitalized) is recommended.



Y Yn , 0.008856



1 3



if



Z Z 16 f Z 5 7.787 · Z 1 116 if n n



The tristimulus values Xn, Yn, Zn define the color of the nominally white object-color stimulus. Usually, the white object-color stimulus is given by the spectral radiant power of one of the CIE standard illuminants, for example, C, D65 or another phase of daylight, reflected into the observer’s eye by the perfect reflecting diffuser. Under these conditions, Xn, Yn, Zn are the tristimulus values of the standard illuminant with Yn equal to 100. 6.2.1 The total color-difference DE*ab between two colors each given in terms of L*, a*, b* is calculated as follows:



Y L* 5 903.3 Y , n



1 3



Y Y 16 f Y 5 7.787 · Y 1 116 n n



1 3



DE*ab 5 =~DL*! 2 1 ~Da*!2 1 ~Db*! 2



X Xn $ 0.008856



if



X X 16 f X 5 7.787 · X 1 116 n n



1 3



X Y Z Xn, Yn, Zn $ 0.008856



1 3



S D S D S D S D S D S D S D S D S D S D S D S D X X f X 5 X n n



(3)



FS D S D G FS D S D G X Xn



where:



S D



b* hab 5 tan2 1 a*



C*ab 5 =~a*!2 1 ~b*!2



(26) (27)



Differences in hue angle °hab between the test specimen and reference can be correlated with differences in their visually perceived hue, except for very dark colors (8). Differences in chroma D°C*ab([C*ab]batch − [C*ab]standard) can similarly be correlated with differences in visually perceived chroma.



(8)



6.2.3 In calculating a* and b*, values of X/Xn, Y/Yn, Z/Zn less than 0.008856, may still be included if the normal 3



D 2244 – 05 ellipses with increases in CIELAB metric chroma C*ab and with respect to changes in CIELAB metric hue angle h*ab. The CMC components and single number tolerances are computed as follows:



6.2.7 For judging the relative contributions of differences in lightness, chroma, and hue to the total color difference between two colors, it is useful to calculate the CIE 1976 metric hue difference °DH*ab between them as follows: DH*ab 5 =~DE* ab! 2 2 ~DL*! 2 2 ~DC* ab! 2



(28)



DECMC ~l : c! 5 cf ·



where DE*ab is calculated as in 6.2.1 and DC*ab is calculated as in 6.2.6; then the equation DE*ab 5 =~DL*! 2 1 ~DC*ab! 2 1 ~DH*ab! 2



a*S · b*B 2 a*B · b*S 0.5 · C* ~ = ab,B · C*ab,S 1 a*B · a*S 1 b*B · b*S !



DL* l · SL



2



DC* 1 c·S c



2



1



DH* SH



2



(31)



The parameters (l, c) are to compensate for systematic bias or parametric effects such as texture and sample separation. The most common values are (2:1) for textiles and plastics that are molded to simulate a woven material, implying that lightness differences carry half the importance of chroma and hue differences (13). The values (1:1), often assumed to represent a just perceptible difference, should be applied to materials that require very critical tolerances or have glossy surfaces. For specimens that are matte, randomly rough, or mildly textured, values intermediate between (1:1) and (2:1) can be used, with the value (1.3:1) being reported most frequently. The parameter cf is a commercial factor (15), used to adjust the total volume of the tolerance region so that accept/reject decisions can be made on the basis of a unit value of the tolerance. The color dependent functions are defined as:



(29)



contains terms showing the relative contributions of lightness differenceD L*, chroma difference DC*ab, and hue difference D° H*ab to the total color differenceD E*ab. This method of computing a metric hue difference loses the information about the sign of the hue difference (positive or negative) and can be unstable for pairs of colors near the neutral axis. An alternative method has been proposed (14) that corrects both problems: DH*ab 5



ŒS D S D S D



(30)



6.3 CMC Color Tolerance Equation—The Colour Measurement Committee of the Society of Dyers and Colourists undertook a task to improve upon the results of the JPC79 tolerance equation (2) developed at J & P Coates thread company in the United Kingdom. It was a combination of the CIELAB equation and local optimization based on the position of the standard used to derive the FMC-2 equation. It was based on the more intuitive perceptual variables of lightness, chroma and hue instead of the lightness, redness/greenness and yellowness/blueness of the older equation. It is intended to be used as a single-number shade-passing equation. There should not be a need to break the equation down into perceptual components—the CIELAB components of the model do that already. Fig. 1 (12) shows the CIELAB chromaticness plane (a*, b*) with a large number of CMC ellipsoids plotted on that plane. The figure clearly shows the change in area of the



SL 5



0.040975 · L* ~1 1 0.01765 · L*! SL 5 0.511,



for



for



L* $ 16



(32)



L*, 16



0.0638 · C* 1 0.638 SC 5 ~1 1 0.0131 · C*! SH 5 SC ~T · f 1 1 2f! where, f5



H



~C*!4 ~C*!4 1 1900



T 5 0.56 1 ?0.2 cos ~h 1 168°!?,



J



1 2



if 164° , h , 345°



else, T 5 0.36 1 ?0.4 cos ~h 1 35°!?



All angles are given in degrees but will generally need to be converted to radians for processing on a digital computer. In Eq 32, the values of L*, C*, and h are taken to be those of the standard specimen. 6.4 CIE94 Color Tolerance Equation (3)—The development of this color tolerance equation was prompted by the success of the CMC tolerance equation. It was derived primarily from visual observations of automotive paints on steel panels. Like, the CMC equation, it is based on the CIELAB color metric and uses the position of the standard in CIELAB color space to derive a set of analytical functions that modify the spacing of the CIELAB space in the region around the standard. Its weighting functions are much simpler than those of the CMC equation. CIE94 tolerances are computed as follows: DE*94 5 kv



1 2



FS D S D S D G DL* kLSL



2



DC* 1 k S C C



2



DH* 1 k S H H



2



(33)



Unlike many previous color difference equation, CIE94 comes with a well defined set of conditions under which the equation will provide optimum results and departures from this



FIG. 1 CMC Ellipse Distribution in the CIELAB (a*, b*) Plane



4



D 2244 – 05 set of conditions will cause the agreement between the visually evaluated color-difference and the computed color-difference to be significantly poorer. Those conditions are given in Table 1. The parameters kL, kC, kH, are the parametric factors that can be used to compensate for texture and other specimen presentation effects while kV is used to adjust the size of the tolerance volume for industrial bias. The parameters SL, SC, SH are used to perform the local distortion of CIELAB color space, again based on the position of the standard specimen in that space. The are computed using the following equations:



Step 2



SL 5 1



Step 3



Chroma C99 5



~loge~1 1 0.045 G!! ~0.045 kCHkE!



(36)



180 Hue angle h99 5 hef p Redness a99 5 C99 cos ~hef! Yellowness b99 5 C99 sin ~hef! Lightness L99 5 105.509 [loge ~1 1 0.0158 L*!# kE



(34)



SC 5 1 1 0.045 · C*



DE99 5 =~DL99!2 1 ~Da99!2 1 ~Db99!2



SH 5 1 1 0.015 · C*



(37)



or



In Eq 34, the value of C* is taken to be that of the standard specimen. 6.5 DIN99 Color Difference Equation—The publication in 1996 of the paper by Rohner and Rich (4) prompted the German standards institute (DIN) to further develop and standardize a modified version as a new color difference formula that globally models color space using logarithms of the CIELAB coordinates rather than the linear and hyperbolic functions of CMC and CIE94. The equations derived and documented in standard DIN 6176 provides an axes rotation and the logarithmic expansion of the new axes to match that of the spacing of the CIE94 color tolerance formula without the need to make the specimen identified as standard the source of the distortion of distances in the CIELAB color space. Also, as neither the tristimulus values XYZ nor the CIELAB axes a*, b* are perceptual variables while the axes L*, C* and h*ab are correlates of the perceptions of lightness, chroma and hue, it seemed appropriate to scale the differences or distances in color space following the Weber-Fechner law of perception. This resulted in a formula which is easy to use and has equivalent performance to CMC or CIE94. It also eliminates the annoying reference-color based distortion of CIELAB. Thus computed color differences are based only on the Euclidean distance in the DIN99 space. The procedures for computing the DIN99 formula are: Step 1 Redness e 5 cos ~16°! a* 1 sin ~16°! b*



DE99 5 =~DL99!2 1 ~DC99!2 1 ~DH99!2 with, DC99 5 C99,B 2C99,S D H99 5



Where subscripts S refers to the product standard and subscript B refers to the current product batch or test sample. Default parameters are: kE = kCH = 1, kE (1 : kCH). For textiles the following equivalence relations holds: To obtain an equivalent computed difference to a CMC (l = 2, c = 1) difference, use the parameters: 2 (1 : 0.5), which indicate that kE = 2 and, kCH = 0.5. 6.6 CIEDE2000 Color Difference Equation (5)—The development of this color difference equation grew out of the research being performed to try to determine which of the two color tolerances equations, CMC or CIE94, was the better formula. In the process, the researchers came to the conclusion that neither formula was truly optimum. Therefore the CIE set up a new technical committee, TC 1-47, Hue & Lightness Dependant Correction to Industrial Colour Difference Equations, to recommend a new equation that addresses the shortcomings in both color tolerance equations. One of the major weaknesses of the color tolerance equations was using the position of the reference color in CIELAB color space for computing the local distortion of CIELAB color space. When the identifications of the two specimens are reversed (calling the original test specimen the reference and the original reference now the test specimen) the computation results in a different computed color difference. This is contrary to what is observed. Visually, there is no change in the magnitude of the difference between the specimens simply by switching roles. By using the position of the arithmetic average color between the two specimens to compute the local distortions to CIELAB color space, the roles of the two specimens may be switched without changing the magnitude of the computed colordifference, in full agreement with the visual assessments. The report from CIE TC 1-47 has shown that CIEDE2000 outperforms both CMC and CIE94 across a wide array of specimens. The CIEDE2000 color differences are computed from the following equations:



(35)



Yellowness f 5 0.7~2sin ~16°! a* 1 cos ~16°! b*! Chroma G 5 ~e2 1 f2!0.5



SD



f Hue angle hef 5 arctan e



TABLE 1 Basis Conditions for CIE94 Tolerance Equation Attribute



Requirement



Illumination Specimen Illuminance Observer Background Viewing Mode Sample Size Sample Separation Size of Color Differences Sample Structure



D65 source 1000 lx Normal color vision Uniform neutral gray L* = 50 Object >4° subtended visual angle Minimum possible 0 to 5 CIELAB units Visually homogenous



~a99,S · b99,B 2 a99,B · b99,S! 0.5 · C ~ = 99,B · C99,S 1 a99,B · a99,S 1 b99,B · b99,S !



L8 5 L*



a8 5 ~1 1 G! · a* C8 5 =a82 1 b82



5



b8 5 b*



(38)



D 2244 – 05



SD



b8 h8 5 arctan a8



S Œ



standard allows a user to predefine the acceptance volume. This is convenient for certain textile sorting applications and for graphical quality control charting. Such a predetermination is not possible with CIEDE2000. Nor is it possible or reasonable to plot groups of colors in terms of the modified space coordinates, L*,a8, b* since the meaning of a8 is determined uniquely for each pair of colors. Thus the equation is highly optimized for pairwise comparison of a product standard to a production test specimen but not for statistical process control.



D



C* 7 C* 1 257 where C* is the arithmetric mean of the CIELAB C* values for the pair of specimens (standard and batch). G 5 0.5 ·



12



7



DL8 5 L8B 2 L8S DC8 5 C8B 2 C8S DH8 5



a8S · b8B 2 a8B · b8S



7. Test Specimens 7.1 This practice does not cover specimen preparation techniques. Unless otherwise specified or agreed, prepare specimens in accordance with appropriate test methods and practices.



=0.5 · ~C8S · C8B 1 a8S · a8B 1 b8S · b8B!



S



DL8 DE002 5 K · S L L



D S



D S D



DC8 1 K ·S C C DC8 · DH8 1 RT · K · S · K · S C C H H 2



S



2



DH8 1 K ·S H H



D



2



D E00 5 =DE002



8. Procedure 8.1 Select appropriate geometric conditions for color measurement in accordance with Practice E 805. 8.2 Operate the instrument in accordance with the manufacturer’s instructions and the procedures given in Practice E 1164. 8.3 When a colorimetric spectrometer is used, obtain the reflectance values of the reference specimen and test specimens, in turn, at a sufficient number of wavelength intervals to permit accurate calculation of CIE tristimulus values. See Practice E 308. 8.4 Measure at least three portions of each specimen surface to obtain an indication of uniformity. Record the location where these measurements were made on the specimen.



The specimen or industry dependent parameters are KL, KC, KH and the color space dependent parameters are SL, SC, SH and RT. The three S terms operate on the, assumed orthogonal, CIELAB coordinates and the RT term computes a rotation of the color difference volume in the blue and purple-blue regions of the CIELAB diagram. The four color space terms are computed as follows: SL 5 1 1



0.015 · ~L8 2 50!2



(39)



=20 1 ~L8 2 50!2



SC 5 1 1 0.045 · C8 SH 5 1 1 0.015 · C8 · T RT 5 –sin ~2· Du! · RC RC 5 2 ·



9. Calculation 9.1 Calculate color-scale values L*, a*, b*, and local tolerance weights (SL, SC, SH) if not obtained automatically. 9.2 Calculate color differences DE*ab,D ECMC and their components, or DE94, DE99, or DE00, if not obtained automatically, as described in 6.2-6.6, respectively.



Œ



C87 7 C8 1 257



SF



Du 5 30 · exp 2



~h8 2 275°! 25



GD 2



T 5 1 2 0.17 · cos ~h8 2 30°! 1 0.24 · cos ~2h8! 1 0.32 · cos ~3h8 1 6°! 2 0.20· cos ~4h8 2 63°!



10. Report 10.1 Report the following information: 10.1.1 Total color difference DECMC, DE94, DE99, or DE00 of each test specimen from its reference. 10.1.2 For CIELAB color differences, L*, a*, b* for the reference, DL*, Da*, Db* and if desired Dhab, DC*ab, and DH*ab for each specimen. 10.1.3 For other color tolerance or color difference metrics, only the CIELAB coordinates should be reported as the local distortions do not necessarily provide continuous, visually correlated parameters.



While not obvious from this listing, all displayed angles are assumed to be given in degrees, including Du and thus must generally be converted into radians for trigonometric analysis on digital computers. 6.6.1 Using the arithmetic average of the CIELAB color coordinates of the reference and test specimens to compute the local distortion of CIELAB color space introduces a new problem. Current color tolerance difference equations which base the distortion of CIELAB space on the position of the



TABLE 2 Precision of Calculated Color Differences Determined for Various Conditions of Measurement and Analysis Measurement Conditions Geometry 45°/0° 45°/0° SphereB SphereB A B



Illuminant



Observer



D65 D65 D65 D65



1964 1964 1964 1964



DE Equation CIELAB CMC(2:1) CIELAB CMC(2:1)



R* is the approximate inter-laboratory precision = 3.0 3 standard deviation. Specular component included for integrating-sphere measurements.



6



No. of Instruments



Mean DE



Standard Deviation



R*A



54 54 282 282



1.05 0.55 1.00 0.53



0.07 0.03 0.06 0.03



0.21 0.09 0.18 0.09



D 2244 – 05 the precision of color and color-difference measurements by sending out pairs of painted chips exhibiting small color differences on a quarterly basis since 1971. In a typical recent survey (Report No. 111, February, 2000), 118 instruments were involved. Table 2 gives the mean color differences and their standard deviations for the groups of instruments considered separately in the intercomparison, together with the conditions of analysis and measurement. 11.2.1 Reproducibility—Based on the between-laboratory standard deviations, two color-difference results, obtained by operators in different laboratories measuring opaque, matte paint on sealed white paper stock should be considered suspect if they differ by more than the values shown in column R* of Table 2. 11.3 Precision—Based on the within-laboratory standard deviations, the precision of color-difference measurements, summarized in Table 2, was equivalent to the precision of measured values of color as reported in the literature (10,11) and is thus likely to be representative of the precision obtainable for all production materials.



10.1.4 For non-uniform specimens, range of colordifference magnitudes obtained for different areas of the specimens. 10.1.5 Description or identification of the method of preparing the specimens. 10.1.6 Identification of the instrument used, by the manufacturer’s name and model number, and the color-scale system used. 11. Precision and Bias 11.1 Since the precision and bias of a test method cannot be separated from the effect of the specimens and materials and since this practice does not address the issues related to the preparation and presentation of specimens, no definitive statement about precision and bias can be made. The next section, uses data from a commercial collaborative testing program to illustrate precision for one material. Because of the many trigonometric functions and power functions involved in computing the color space parameters, all computations should be carried out in IEEE floating point format to greatest number of bits of precision available on the computational system, usually known as double precision. 11.2 The Collaborative Testing Services Color and Color Difference Collaborative Reference Program (9) has surveyed



12. Keywords 12.1 color; color difference; color metrics; color spaces; color tolerances



APPENDIXES (Nonmandatory Information) X1. COLOR SPACES AND COLOR DIFFERENCE METRICS NO LONGER RECOMMENDED FOR NEW USERS TABLE X1.1 Some Selected Values of Ka and Kb for Various CIE Standard Observers and CIE Standard and Recommended Illuminants



X1.1 Hunter LH, aH, bH Color Space and Color-Difference Equation—This approximately uniform color space (16) is produced by plotting in rectangular coordinates the quantities LH, aH, bH calculated as follows:



a H 5 Ka



b H 5 Kb



1 2



S D S D S D S D S D S D S D



Y LH 5 100 Y n



X Y Xn – Yn Y Yn



1 2



Y Z Yn – Zn Y Yn



1 2



Illuminant/Observer A – 1931 2° A –1964 10° C – 1931 2° C – 1964 10° D50 – 1931 2° D50 – 1964 10° D55 – 1931 2° D55 – 1964 10° D65 – 1931 2° D65 – 1964 10° D75 – 1931 2° D75 – 1964 10° F2 –1931 2° F2 – 1964 10° F7 – 1931 2° F7 – 1964 10° F11 – 1931 2° F11 – 1964 10°



(X1.1)



(X1.2)



(X1.3)



where X, Y, and Z are CIE daylight tristimulus values obtained from a measurement or other source and Ka and Kb are coefficients that vary with the illuminant-observer combination to which the tristimulus values refer. In general, Ka 5 175 ~Xn/98.074!1 / 2 and Kb 5 70 ~Zn/118.232!1 / 2 where Xn and Zn are the X and Z tristimulus values for the perfect reflecting diffuser in the chosen illuminant-observer combination. Examples of Ka and Kb are tabulated in Table X1.1.



Ka



Kb



185.21 186.30 175.00 174.30 173.52 173.79 172.85 172.96 172.28 172.06 172.21 171.71 175.99 179.58 172.27 172.95 177.56 180.09



38.403 38.195 70.000 63.379 58.481 58.092 61.798 61.387 67.175 66.687 71.292 70.710 52.849 53.486 67.133 66.805 51.642 52.144



X1.1.1 The total color-difference DEH between two colors each given in LH, aH, bH is calculated as follows: 1



DEH 5 [~DLH!2 1 ~DaH!2 1 ~DbH!2#2



7



(X1.4)



D 2244 – 05 where: DLH 5 LH,B – LH,S



(X1.5)



DaH 5 aH,B – aH,S



(X1.6)



DbH 5 bH,B – bH,S



(X1.7)



where LH,S, aH,S, bH,S refer to the reference or standard and LH,B, aH,B, bH,B refer to the test specimen or batch. The signs of the components DLH, D aH, DbH have the same approximate meaning as do their counterparts in 6.2.5.



X2. EXAMPLE CALCULATIONS FOR COLOR TOLERANCE EQUATIONS



TABLE X2.1 Example Calculations for Color Tolerance Equations Color Coordinate X Y Z L* a* b* C* hab* SLCMC SCCMC f T SHCMC DL* DC* DH* DE*ab DECMC(1:1) DECMC(2:1) SL94 SC94 SH94 DE94 e f G hef kE kCH C99 h99 a99 b99 L99 DE99(Lab) DC99 DH99 DL99 DE99(LCH) L*ave C*ave G a8 C8 h8 C8ave h8ave DL* DC8 DH’ SL SC SH RC Du RT T DE00



STD-1



BAT-1



STD-2



BAT-2



STD-3



BAT-3



STD-4



BAT-4



STD-5



BAT-5



19.4100 28.4100 11.5766 60.2574 -34.0099 36.2677 49.7194 133.160 1.1965 2.5589 0.9998 0.7515 1.9231



19.5525 28.6400 10.5791 60.4626 -34.1751 39.4387 52.1857 130.910



22.4800 31.6000 38.4800 63.0109 -31.0961 -5.8663 31.6447 190.683 1.2224 2.0653 0.9991 0.7599 1.5700



22.5833 31.3700 36.7901 62.8187 -29.7946 -4.0864 30.0735 187.810



28.9950 29.5800 35.7500 61.2901 3.7196 -5.3901 6.5490 304.609 1.2064 1.0228 0.7014 0.6369 0.7623



28.7704 29.7400 35.6045 61.4292 2.2480 -4.9620 5.4474 294.373



4.1400 8.5400 8.0300 35.0831 -44.1164 3.7933 44.2792 175.086 0.8878 2.4259 0.9998 0.7513 1.8229



4.4129 8.5100 8.6453 35.0232 -40.0716 1.5901 40.1031 177.728



4.9600 3.7200 19.5900 22.7233 20.0904 -46.6940 50.8326 293.280 0.6646 2.5848 0.9999 0.5991 1.5487



4.6651 3.8100 17.7848 23.0331 14.9730 -42.5619 45.1188 289.382



0.2052 2.4663 -1.9999 3.1819 1.4282 1.4205 1.0000 3.23737 1.74579 -22.6983 30.9657 38.3939 126.242 1 1 22.2993 2.20334 -13.1833 17.9850 70.5738



60.3600 50.9525 0.0017 -34.0678 49.7590 133.21 50.9914 132.084 0.2052 2.4648 -2.0018 1.1427 3.2946 1.9951 1.9932 0.0000 0.0000 1.3010 1.2644



-0.1922 -1.5712 -1.5472 2.2134 1.2549 1.2474 1.00000 2.42401 1.47467



1.3910 -21.9832 33.1313 39.7611 123.565 1 1 22.7950 2.15662 -12.6029 18.9941 70.7489 1.1772 0.49568 -1.05329 0.17512 1.1772



-34.2333 52.2238 130.96



-31.5095 2.05161 31.5762 176.275 1 1 19.6478 3.07657 -19.6063 1.27658 72.8994



62.9148 30.8591 0.0490 -32.6195 33.1428 190.20 32.3315 188.822 -0.1922 -1.6226 -1.5490 1.1831 2.4549 1.4560 1.8527 0.0002 0.0000 0.9402 1.2630



0.1391 -1.1016 -1.0657 1.5390 1.7684 1.7656 1.00000 1.29470 1.09824



1.2481 -29.7677 2.99825 29.9184 174.249 1 1 18.9522 3.04121 -18.8568 1.89928 72.7388 0.98756 -0.69558 -0.68237 -0.16065 0.98756



-31.2542 31.5202 187.45



2.09015 -4.34462 4.82125 295.692 1 1 4.36339 5.16080 1.89166 -3.93203 71.4521



61.3597 5.9982 0.4966 5.5669 7.7488 315.92 6.8719 310.031 0.1391 -1.7538 -1.3995 1.1586 1.3092 1.0717 0.0218 4.2110 -0.0032 0.6952 1.8731



8



-0.0599 -4.1761 1.9430 4.6063 2.0258 2.0250 1.00000 2.99256 1.66419



1.2980 0.79346 -3.77258 3.85513 281.878 1 1 3.55497 4.91969 0.73168 -3.47886 71.5698 1.25091 -0.80842 -0.94729 0.11774 1.25091



3.3643 5.9950 304.14



-41.3637 11.0634 42.8177 165.026 1 1 23.8646 2.88024 -23.0542 6.16626 46.5330



35.0532 42.1911 0.0063 -44.3939 44.5557 175.12 42.4554 176.429 -0.0599 -4.2007 1.9430 1.2148 2.9105 1.6476 1.9759 0.0000 0.0000 1.0168 1.8645



0.3098 -5.7138 -3.2580 6.5847 3.0870 3.0604 1.00000 3.28747 1.76249



1.8204 -38.0826 8.80059 39.0863 166.988 1 1 22.5517 2.91449 -21.9726 5.07769 46.4688 1.53592 -1.31296 0.79439 -0.06425 1.53592



-40.3237 40.3550 177.74



6.44406 -35.2962 35.8796 280.347 1 1 21.3579 4.89297 3.83592 -21.0106 32.3670



22.8782 47.9757 0.0026 20.1424 50.8532 293.33 47.9924 291.381 0.3098 -5.7215 -3.2653 1.4014 3.1597 1.2617 1.9897 19.5282 -1.2537 0.3636 2.0373



2.5561 2.66348 -31.5285 31.6408 274.829 1 1 19.6745 4.79667 1.65617 -19.6046 32.7463 2.62143 -1.68341 -1.97335 0.37933 2.62143



15.0118 45.1317 289.43



D 2244 – 05 Color Coordinate X Y Z L* a* b* C* hab* SL SC f T SH DL* DC* DH* DE*ab DECMC(1:1) DECMC(2:1) SL94 SC94 SH94 DE94 e f G hef kE kCH C99 h99 a99 b99 L99 DE99(Lab) DC99 DH99 DL99 DE99 L*ave C*ave G a8 C8 h8 C8ave h8ave DL* DC8 DH8 SL SC SH RC Du RT T DE00



STD-6 15.6000 9.2500 5.0200 36.4612 47.8580 18.3852 51.2680 21.0148 0.9090 2.5947 0.9999 0.5836 1.5144



BAT-6 15.9148 9.1500 4.3872 36.2715 50.5065 21.2231 54.7844 22.7924



STD-7 73.0000 78.0500 81.8000 90.8027 -2.0831 1.4410 2.5329 145.326 1.4295 0.7944 0.1456 0.7600 0.7666



-0.1897 3.5164 1.6441 3.8864 1.7490 1.7396 1.00000 3.30706 1.76902 51.0729 3.13861 51.1692 3.51660 1 1 26.5492 0.06138 26.4992 1.62847 48.0009



36.3664 53.0262 0.0013 47.9197 51.3256 20.99 53.0850 21.8781 -0.1897 3.5189 1.6444 1.1943 3.3888 1.7357 1.9949 0.0000 0.0000 0.9239 1.4146



BAT-7 73.9351 78.8200 84.5156 91.1528 -1.6435 0.0447 1.6441 178.441



0.3501 -0.8888 1.1631 1.5051 1.9009 1.8890 1.00000 1.11398 1.03799



1.4249 54.4010 4.53729 54.5899 4.76770 1 1 27.5616 0.08321 27.4662 2.29081 47. 8000 1.18914 1.01234 0.59066 -0.20088 1.18914



50.5717 54.8444 22.77



STD-8 73.9950 78.3200 85.3060 90.9257 -0.5406 -0.9208 1.0677 239.583 1.4303 0.7052 0.0261 0.6949 0.6996



-1.60532 1.37149 2.11140 139.491 1 1 2.01703 2.43458 -1.53356 1.31019 93.8837



90.9778 2.0885 0.4999 -3.1244 3.4407 155.24 2.9531 167.101 0.3501 -0.9751 1.1972 1.6110 1.1329 1.0511 0.0011 0.0000 0.0000 1.1546 1.4440



BAT-8 69.1762 73.4000 79.7130 88.6381 -0.8985 -0.7239 1.1538 218.857



-2.2876 0.0861 -0.3993 2.3238 1.7026 0.9901 1.00000 1.04805 1.01602



1.4194 -1.56759 0.34716 1.60557 167.513 1 1 1.55022 2.92365 -1.51355 0.33520 94.1231 1.00416 -0.46681 0.85621 0.23942 1.00416



-2.4651 2.4655 178.96



STD-9 0.7040 0.7500 0.9720 6.7747 -0.2909 -2.4247 2.4421 263.160 0.5110 0.7890 0.1356 0.6246 0.7488



-0.77341 -0.51529 0.92934 213.674 1 1 0.91044 3.72931 -0.75767 -0.5048 93.9679



89.7819 1.1108 0.5000 -0.8108 1.2269 228.63 1.3784 218.436 -2.2876 0.3029 -0.4850 1.5930 1.0620 1.0288 0.0001 0.1794 0.0000 1.3916 1.5381



BAT-9 0.6139 0.6500 0.8510 5.8714 -0.0974 -2.2282 2.2303 267.469



-0.9033 -0.2117 0.1766 0.9441 1.8034 0.9533 1.00000 1.10989 1.03663



2.3226 -1.06323 -0.31376 1.10855 196.441 1 1 1.08179 3.42855 -1.03756 -0.30618 92.3911 1.61372 0.17135 -0.29736 -1.5768 1.61372



-1.3477 1.5298 208.24



STD-10 0.2200 0.2300 0.3250 2.0776 0.0795 -1.1350 1.1378 274.004 0.5110 0.7095 0.0279 0.5878 0.7008



-0.94785 -1.57548 1.83863 238.968 1 1 1.76652 4.17078 -0.91067 -1.51369 10.7292



6.3231 2.3362 0.4999 -0.4363 2.4637 259.80 2.3483 263.02 -0.9033 -0.2306 0.2638 1.6517 1.1057 1.0336 0.0005 23.848 -0.0004 0.9549 0.6386



BAT-10 0.0933 0.1000 0.1452 0.9033 -0.0621 -0.5515 0.5550 263.419



-1.1743 -0.5828 -0.1444 1.3189 2.4491 1.4274 1.00000 1.05120 1.01707



0.9388 -0.70772 -1.48059 1.64104 244.452 1 1 1.58328 4.26650 -0.68281 -1.42847 9.36013 1.39052 -0.18325 0.16002 -1.36907 1.39052



-0.1461 2.2330 266.25



-0.23643 -0.77907 0.81415 253.118 1 1 0.79959 4.41774 -0.2322 -0.76514 3.40777



1.4905 0.8464 0.5000 0.1192 1.1412 275.99 0.8503 268.20 -1.1743 -0.5819 -0.2165 1.7246 1.0383 1.0099 0.0000 27.865 0.0000 0.7787 0.9076



1.3063 -0.21163 -0.35911 0.41684 239.488 1 1 0.41297 4.17986 -0.20967 -0.35579 1.49518 1.95603 -0.38662 -0.13638 -1.91259 1.95603



-0.0931 0.5593 260.42



If Table X2.1 is used to check a computer program, discrepancies of 60.0001 and occasionally 6 0.00002 may arise due to roundoff, and do not call into question the program’s correctness.



9



D 2244 – 05 REFERENCES (1) “Official Recommendations on Uniform Color Spaces, Color Difference Equations, and Psychometric Color Terms,” Supplement 2 to CIE Publication No. 15 (E-1.3.1) 1971, Colorimetry (incorporated into CIE Publication No. 15.2 (TC-1.3) 1986, Colorimetry, 2nd ed.), Bureau Central de la CIE, Paris, 1978. (Available from CIE Publications, c/o TLA Lighting Consultants, Inc., 7 Pond Street, Salem, MA 01970.) (2) Clark, F. J. J., McDonald, R., and Rigg, B., “Modification to the JPC 79 Colour-Difference Formula,” Journal of the Society of Dyers and Colorists, Vol 100, 1984, pp. 128-132. (3) Commission Internationale de l’Èclairage, Technical Report 116, Industrial Colour-Difference Evaluation, Central Bureau of the CIE, Vienna, 1995. (Available from CIE Publications, c/o TLA Lighting Consultants, Inc., 7 Pond Street, Salem, MA 01970.) (4) Rohner, E., und Rich, Danny C., “Eine angenähert gleichförmige Metrik für industrielle Farbtoleranzen von Körberfarben,” Die Farbe, 42, Heft 4-6, 1996, pp. 207-220. (5) Commission Internationale de l’Èclairage, Technical Report 142-2001, Improvement to Industrial Colour Difference Equation, Central Bureau of the CIE, Vienna, 2000. (Available from CIE Publications, c/o TLA Lighting Consultants, Inc., 7 Pond Street, Salem, MA 01970.) (6) Robertson, A. R., “The CIE 1976 Color-Difference Formulae,” Color Research and Application, Vol 2, 1977, pp. 7–11. (7) McLaren, K., and Taylor, P. F., “The Derivation of Hue-Difference Terms from CIELAB Coordinates,” Color Research and Application, Vol 6, 1981, pp. 75–77.



(8) McLaren, K., “CIELAB Hue-Angle Anomalies at Low Tristimulus Ratios,” Color Research and Application, Vol 5, 1980, pp. 139–143. (9) “Color and Appearance Collaborative Reference Program for Color and Color-Difference,” Collaborative Testing Services, Inc., McLean, VA. (10) Billmeyer, F. W., Jr., and Alessi, P. J., “Assessment of ColorMeasuring Instruments,” Color Research and Application, Vol 6, 1981, pp. 195–202. (11) Rich, D. C., “Colorimetric Repeatability and Reproducibility of CHROMA-SENSOR Spectrocolorimeters,” DIE FARBE, Vol 37, 1990, pp. 247-261. (12) McDonald, Roderick, “Color Communication in the 90s,” Textile Chemist and Colorist, Vol 24, No 4, 1992, pp. 11-15. (13) Commission Internationale de l’Èclairage, Technical Report 101, Parametric effects in colour-difference evaluation, Central Bureau of the CIE, Vienna, 1993. (Available from CIE Publications, c/o TLA Lighting Consultants, Inc., 7 Pond Street, Salem, MA 01970.) (14) “Practical Formula for the Computation of CIE 1976 Hue Difference,” Color Research and Application, 21, 1996, p. 314. (15) AATCC Test Method 173-1992, “CMC: Calculation of Small Color Differences for Acceptability,” AATCC Technical Manual, AATCC Research Triangle Park, NC, 1993. (16) Hunter, R. S. and Harold, R. W., The Measurement of Appearance, 2nd Ed. Wiley-Interscience, New York, NY, 1987, pp. 148–152.



SUMMARY OF CHANGES Committeee 1E12 has identified the location of selected changes to this standard since the last issue (D 2244 – 02 ) that may impact the use of this standard. (2) Some tristimulus values for STD-9, BAT-9, and BAT-10 in Table X2.1 have been revised.



(1) Effective with this revision of Practice D 2244, the Hunter LH, aH, bH system for colorimetry, formerly documented only for CIE 1931 Standard Observer and Illuminant C, has been revised to reflect calculation in additional illuminant-observer combinations.



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